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A331088
Positive numbers k such that -k is a negative negaFibonacci-Niven number, i.e., divisible by the number of terms in its negaFibonacci representation (A331084).
7
1, 2, 3, 4, 6, 8, 12, 15, 16, 18, 20, 21, 22, 24, 27, 30, 36, 42, 44, 45, 48, 50, 51, 54, 55, 56, 57, 58, 60, 66, 72, 75, 76, 80, 84, 90, 92, 96, 100, 104, 105, 108, 110, 111, 112, 115, 116, 120, 124, 126, 128, 129, 132, 136, 138, 141, 142, 144, 150, 152, 153, 156, 168, 170, 172, 175, 176, 180, 184, 186, 190, 192, 196, 198
OFFSET
1,2
COMMENTS
The k-th Fibonacci number is a term for all even k, since its negaFibonacci representation is 1 followed by (k-1) zeros.
LINKS
EXAMPLE
4 is a term since the negaFibonacci representation of -4 is 1010 whose sum of digits is 1 + 0 + 1 + 0 = 2 which is a divisor of 4.
MATHEMATICA
ind[n_] := Floor[Log[Abs[n]*Sqrt[5] + 1/2]/Log[GoldenRatio]];
f[1] = 1; f[n_] := If[n > 0, i = ind[n - 1]; If[EvenQ[i], i++]; i, i = ind[-n]; If[OddQ[i], i++]; i];
negaFibTermsNum[n_] := Module[{k = n, s = 0}, While[k != 0, i = f[k]; s += 1; k -= Fibonacci[-i]]; s];
Select[Range[200], Divisible[#, negaFibTermsNum[-#]] &]
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Jan 08 2020
STATUS
approved